BOUNDARY CONTROL AND A MATRIX INVERSE PROBLEM FOR THE EQUATION $ u_{tt}-u_{xx}+V(x)u=0$

Abstract

The authors solve the problem of recovering the matrix-valued potential , , from the given reaction operator , . They show the connections between this problem and the theory of boundary control, which allows them to obtain analogues of the classical Gel'fand-Levitan-Krein equations. They establish the basis property for a family of vector-valued exponentials; this property is connected with the spectral characteristics of the boundary value problem. They prove the controllability of the corresponding system under a boundary control .